The invention relates to acoustic systems including a duct guiding an acoustic wave propagating longitudinally therethrough and having higher order mode transverse modal energy, and more particularly to a system suppressing detection of such energy.
The invention arose during continuing development efforts relating to active acoustic attenuation systems, including the subject matter shown and described in U.S. Pat. Nos. 4,665,549, 4,677,676, 4,677,677, 4,736,431, 4,815,139, 4,837,834, 4,987,598, 5,022,082, and 5,022,082, and allowed U.S. application Ser. No. 07/468,590, filed Jan. 23, 1990, all assigned to the assignee of the present invention and incorporated herein by reference.
A sound wave propagating axially through a rectangular duct has a cut-off frequency f.sub.c =c/2L where c is the speed of sound in the duct and L is the longer of the transverse dimensions of the duct. Acoustic frequencies below the cut-off frequency f.sub.c provide plane and uniform pressure acoustic waves extending transversely across the duct at a given instant in time. Acoustic frequencies above f.sub.c allow non-uniform pressure acoustic waves in the duct due to higher order modes.
For example, an air conditioning duct may have transverse dimensions of two feet by six feet. The longer transverse dimension is six feet. The speed of sound in air is 1,130 feet per second. Substituting these quantities into the above equation yields a cut-off frequency f.sub.c of 94 Hertz.
In circular ducts similar considerations apply when the duct diameter is approximately equal to one-half of the wavelength. Exact equations may be found in "Higher Order Mode Effects in Circular Ducts and Expansion Chambers", L. J. Eriksson, Journal of Acoustic Society of America, 68(2), August 1980, pp. 545-550.
Active attenuation involves injecting a canceling acoustic wave to destructively interfere with and cancel an input acoustic wave. In the given example, the acoustic wave can be presumed as a plane uniform pressure wave extending transversely across the duct at a given instant in time only at frequencies less than 94 Hertz. At frequencies less than 94 Hertz, there is less than a half wavelength across the longer transverse dimension of the duct. At frequencies above 94 Hertz, the wavelength becomes shorter and there is more than a half wavelength across the duct, i.e. a higher order mode with a non-uniform sound field may propagate through the duct.
In an active acoustic attenuation system, the output acoustic wave is sensed with an error microphone which supplies an error signal to a control model which in turn supplies a correction signal to a canceling loudspeaker which injects an acoustic wave to destructively interfere with the input acoustic wave and cancel same such that the output sound at the error microphone is zero. If the sound wave traveling through the duct is a plane wave having uniform pressure across the duct, then it does not matter where the canceling speaker and error microphone are placed along the cross section of the duct. In the above example for a two foot by six foot duct, if a plane wave with uniform pressure is desired, the acoustic frequency must be below 94 Hertz. If it is desired to attenuate higher frequencies using plane uniform pressure waves, then the duct must be split into separate ducts of smaller cross section or the duct must be partitioned into separate chambers to reduce the longer transverse dimension L to less than c/2f at the frequency f that is to be attenuated.
In the above example, splitting the duct into two separate ducts with a central partition would yield a pair of ducts each having transverse dimensions of two feet by three feet. Each duct would have a cut-off frequency f.sub.c of 188 Hertz.
The above noted approach to increasing the cut-off frequency f.sub.c is not economically practicable because active acoustic attenuation systems are often retrofitted to existing ductwork, and it is not economically feasible to replace an entire duct with separate smaller ducts or to insert partitions extending through the duct to provide separate ducts or chambers.
One solution to the above noted problem is shown and described in above incorporated U.S. Pat. No. 4,815,139. The present invention provides another solution.
In the present invention, higher order modes are permitted in the duct, but measurement thereof is prevented, or at least minimized. Rather than allowing the control system to observe transverse energy which it cannot control, the invention instead suppresses detection of transverse modal energy to avoid observation thereof. Since the control system does not observe higher order modes, it does not generate same.
The invention can be used with modes that have non-uniform pressure distribution in both transverse dimensions of a rectangular or other shape duct. The invention may also be used with modes that have non-uniform pressure distribution in both the radial and circumferential dimensions of a circular duct. The invention has application in areas other than active noise control, for example active vibration control, impedance tube acoustical measurements, or other applications where it is desired to suppress detection of higher order modes.